I like how Muslims strongly promote the fact that Islam is a logical faith, and how they will point to the signs in the creation as evidence of a higher power. I've even heard some converts to Islam discuss one thing they loved about the faith: that they didn't have to "just believe" in it. That's from some people who, when asking in particular about the Trinity, received run-around answers eventually telling them they just had to believe it, even though it didn't make sense.
But some Christians caught on to this, and starting accusing Muslims of holding illogical beliefs. For example, the story of the Israa' and Mi'raaj. But a person doesn't start believing Islam because of Israa' and Mi'raaj, whereas the Trinity is a fundamental tenet of Christianity. So while the Israa' and Mi'raaj isn't the sort of thing which makes logical sense, Muslims believe it because they believe in the Prophet Muhammad (saws) and they believe in the Qur'an. The enemies of Islam, when they started hearing this story, began to mock the Prophet (saws) and when someone asked Abu Bakr, challenging his faith, he declared that if the Prophet (saws) said it, then he, Abu Bakr, believed it. What faith! It was proof enough for him that the Prophet (saws) said so.
But still, what brings people to Islam is not this story at all--what brings people to Islam by and large is belief in God in the first place. That's what Islam is about, and that's what is so reasonable and logical about Islam. One God--it makes plenty of sense.
That doesn't mean that we as Muslims understand absolutely everything. It doesn't mean we understand the wisdom behind everything that we do. Some actions might seem extremely illogical--but it's clear that they are part of Islam. We believe that there is wisdom behind it, and we do it to demonstrate our obedience to God.
For example, Muslims are supposed to wash their feet as part of ritual purification before prayer. However, if one is wearing socks (given some prerequisites I won't elaborate on here), then he may simply wipe over the socks instead of washing his feet. But what would seem logical would be to wipe the bottom of the sock, right? But actually, Muslims wipe the top of the foot when they do this, as according to the teachings of the Prophet Muhammad (saws). What sense does it make? The point here is that Muslims do it out of obedience.
A person is not going to come to the conclusion one day, on his own, that after he goes to the bathroom he should wipe the top of his shoes or socks. But Muslims do it--why? Obedience. They have been taught this, and so when they hear a command they reply, "We hear, and we obey."
I don't think that's at all like a belief in the Trinity, which is essential and underlying in Christianity.
The logical part about Islam--the part that makes sense anyway you slice it, the part that doesn't require you to "just believe," is tawheed. Maybe faith on its own is mysterious or cryptic, but belief in One God is the most sensible and reaosnable thing to believe, which I attribute to the fitrah--that we are inclined to believe it anyway, something He has put in us. But just because we can't understand every little detail about a ruling in Islam is not a shortcoming--we should trust in Allah's wisdom and understand that we are to be obedient.